Covariant definition of double null data and geometric uniqueness of the characteristic initial value problem

Mars, Marc; Sánchez-Pérez, Gabriel

doi:10.1088/1751-8121/acd312

Cited by 6 publications

(4 citation statements)

References 18 publications

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“…We also establish the connection between the intrinsic and extrinsic (embedding) pictures. Similar results have been obtained by Mars, Sánchez-Pérez, and Manzano [81][82][83], who developed the intrinsic geometry of hypersurfaces of arbitrary causal type, referred to as the geometrical hypersurface data formalism. Additionally, we include the expressions for all components of the Einstein equation, the general symmetries of a stretched horizon beyond the tangential ones, and the corresponding Noether charges.…”

Section: Introductionsupporting

confidence: 81%

“…In Section 3, we consider a family of sCarrollian structures sC r = (v i (r), k j (r), h ij (r), ρ(r)) labeled by the function r. The stretched horizon with different r can now be considered the leaves of the r = constant foliation of the surrounding spacetime. By utilizing the Mars-Senovilla rigging technique [79,80] (see also [38,96] for situations involving null surfaces), we explicitly establish the correspondence between the two viewpoints and derive the relations between the sCarrollian structure and the rigging structure, including the sCarrollian connection and the sCarrollian stress tensor (see also [81][82][83]). We also discuss the arbitrariness in the embedding of the sCarrollian structure into the spacetime, leading to more general gauge fixings than those adopted in [1].…”

Section: Summary Of the Resultsmentioning

confidence: 99%

“…Stretched horizon embedding: The perspective we advocate in our work [1,72,73] (also see the works by Mars et al [81][82][83]) is to understand the family of sCarrollian structures as a foliation of spacetime near a given null hypersurface in terms of causal hypersurfaces. This establishes an equivalence between the stretched horizon and the sCarrollian perspectives.…”

Section: Rigging Structurementioning

confidence: 99%

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Carrollian hydrodynamics from symmetries

Freidel¹,

Jai-akson²

2023

Class. Quantum Grav.

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In this work, we revisit Carrollian hydrodynamics, a type of non-Lorentzian hydrodynamics which has recently gained increasing attentions due to its underlying connection with dynamics of spacetime near null boundaries, and we aim at exploring symmetries associated with conservation laws of Carrollian ﬂuids. With an elaborate construction of Carroll geometries, we generalize the Randers-Papapetrou metric by incorporating the ﬂuid velocity ﬁeld and the sub-leading components of the metric into our considerations and we argue that these two additional ﬁelds are compulsory phase space variables in the derivation of Carrollian hydrodynamics from symmetries. We then present a new notion of symmetry, called the near-Carrollian diﬀeomorphism, and demonstrate that this symmetry consistently yields a complete set of Carrollian hydrodynamic equations. Furthermore, due to the presence of the new phase space ﬁelds, our results thus generalize those already presented in the previous literatures. Lastly, the Noether charges associated with the near-Carrollian diﬀeomorphism and their time evolutions are also discussed.

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Section: Introductionsupporting

confidence: 81%

Section: Summary Of the Resultsmentioning

confidence: 99%

Section: Rigging Structurementioning

confidence: 99%

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Carrollian hydrodynamics from symmetries

Freidel¹,

Jai-akson²

2023

Class. Quantum Grav.

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“…The maximal globally hyperbolic solution is uniquely determined by the data, up to isometry. This can be seen by first noting that the local solution is defined uniquely, up to isometry, by the data listed; see [42] for an extensive discussion. Choosing a spacelike Cauchy hypersurface within the domain of existence of the coordinate solution, one can appeal to the usual Choquet-Bruhat-Geroch uniqueness theorem for the spacelike Cauchy problem to conclude.…”

Section: The Existence Theorem For Two Null Hypersurfaces Intersectin...mentioning

confidence: 99%

Gluing variations

Chruściel

Cong

2023

Class. Quantum Grav.

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We establish several results on gluing/embedding/extending geometric structures in vacuum spacetimes with a cosmological constant in any spacetime dimensions d ≥ 4, with emphasis on characteristic data. A useful tool is provided by the notion of submanifold-data of order k. As an application of our methods we prove that vacuum Cauchy data on a spacelike Cauchy surface with boundary can always be extended to vacuum data defined beyond the boundary.

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Null Raychaudhuri: canonical structure and the dressing time

Ciambelli,

Freidel,

Leigh

2024

J. High Energ. Phys.

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We initiate a study of gravity focusing on generic null hypersurfaces, non-perturbatively in the Newton coupling. We present an off-shell account of the extended phase space of the theory, which includes the expected spin-2 data as well as spin-0, spin-1 and arbitrary matter degrees of freedom. We construct the charges and the corresponding kinematic Poisson brackets, employing a Beltrami parameterization of the spin-2 modes. We explicitly show that the constraint algebra closes, the details of which depend on the non-perturbative mixing between spin-0 and spin-2 modes. Finally we show that the spin zero sector encodes a notion of a clock, called dressing time, which is dynamical and conjugate to the constraint.It is well-known that the null Raychaudhuri equation describes how the geometric data of a null hypersurface evolve in null time in response to gravitational radiation and external matter. Our analysis leads to three complementary viewpoints on this equation. First, it can be understood as a Carrollian stress tensor conservation equation. Second, we construct spin-0, spin-2 and matter stress tensors that act as generators of null time reparametrizations for each sector. This leads to the perspective that the null Raychaudhuri equation can be understood as imposing that the sum of CFT-like stress tensors vanishes. Third, we solve the Raychaudhuri constraint non-perturbatively. The solution relates the dressing time to the spin-2 and matter boost charge operators.Finally we establish that the corner charge corresponding to the boost operator in the dressing time frame is monotonic. These results show that the notion of an observer can be thought of as emerging from the gravitational degrees of freedom themselves. We briefly mention that the construction offers new insights into focusing conjectures.

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Covariant definition of double null data and geometric uniqueness of the characteristic initial value problem

Cited by 6 publications

References 18 publications

Carrollian hydrodynamics from symmetries

Carrollian hydrodynamics from symmetries

Gluing variations

Null Raychaudhuri: canonical structure and the dressing time

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